Even [a,b]-factors in graphs
Let a and b be integers 4 ≤ a ≤ b. We give simple, sufficient conditions for graphs to contain an even [a,b]-factor. The conditions are on the order and on the minimum degree, or on the edge-connectivity of the graph.
Decomposition of multigraphs
In this note, we consider the problem of existence of an edge-decomposition of a multigraph into isomorphic copies of 2-edge paths . We find necessary and sufficient conditions for such a decomposition of a multigraph H to exist when (i) either H does not have incident multiple edges or (ii) multiplicities of the edges in H are not greater than two. In particular, we answer a problem stated by Z. Skupień.
Minimum survivable graphs with bounded distance increase.
Generalized connected domination in graphs.
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